Page 26 - 83 basic knowledge of astronomy

by assuming thermodynamic equilibrium. However, the resulting equations
above do not contain any quantity characteristic of thermodynamics. This
means that the equations must hold universally, irrespective of whether the
condition of thermodynamic equilibrium is fulfilled. These relationships are
determined by the microscopic interactions between a photon and a particle,
and are not influenced by the environment (temperature, pressure, ... etc.).
We obtained the relationships under the assumption of thermodynamic equi-
librium, where it is most easily derived. Analogously, if you find a big hole
in a road in daytime, you would assume that the hole still exists at night,
when you cannot see it well.

9.8 Another Important Quantity in Radio Astronomy

Brightness Temperature
The brightness temperature T B of a source with monochromatic intensity
(or surface brightness) I ν , is a quantity which is defined by the equation:

c 2
T B = I ν . (35)
2kν 2

This is a quantity with the dimension of temperature obtained by a ‘forced’
application of the Rayleigh–Jeans formula to the radiation from any radio
source. If the radiation comes from a sufficiently hot (T 10 K) thermal
source, without noticeable absorption or additional emission along the prop-
agation path, the brightness temperature must correspond to the physical
temperature of the source. If the source is non–thermal, the brightness tem-
perature has no relevance to any real temperature. For example, for some
maser sources, the brightness temperature could be as high as 10 14 K, al-
though the physical temperature values of the ‘masing’ (i.e. maser–emitting)
gas clouds are only several hundreds of Kelvin. The word ‘brightness tem-
perature’ is a jargon term which is used only, but quite frequently, in radio
astronomy.

10 Radiative Transfer

10.1 Phenomenological Derivation of the Radiative Trans-

fer Equation

Radiative transfer theory describes how the intensity varies as radiation prop-
agates in an absorbing and/or emitting medium. The equation of radiative
transfer can be phenomenologically derived as follows:

26